Why inflation targeting central banks seem to follow a standard Taylor rule

Studies on central bank reaction functions find that central banks only caring about inflation stability, like the ECB, seem to follow a standard Taylor rule in the sense that the interest rate reacts significantly to variations in the output gap. We explain this result by claiming that the alleged reaction to the output gap could in fact be a reaction of the nominal interest rate to variations in the natural real rate of interest, which monetary policy should take into account. This provides a rationale for central banks to observe the output gap in the conduct of purely inflation targeting monetary policy.